Gina Vitale has just contracted to sell a small parcel of land that she inherite
ID: 2617562 • Letter: G
Question
Gina Vitale has just contracted to sell a small parcel of land that she inherited a few days ago. The buyer is willing to pay
?$19,471 at the closing of the transaction or will pay the amounts shown in the following? table, at the beginning of each of the next five years. Because Gina? doesn't really need the money? today, she plans to let it accumulate in an account that earns 4?% annual interest. Given her desire to buy a house at the end of five years after closing on the sale of the? lot, she decides to choose the payment alternative—?$19,471 single amount or the mixed stream of payments in the table—that provides the higher future value at the end of 5 years. Which alternative will she? choose?
Table:
Beginning of Year Cash Flow
1 $4,000
2 $4,000
3 $7,000
4 $2,000
5 $8,000
Explanation / Answer
Option – 1, If Gina Vitale chooses the Lump sum payment Option
Future Value = P x [ Future Value Factor]
= $19,471 x [FVF 4%, 5 Years]
= $19,471 x 1.2166529
= $23,689
Option – 2, If Gina Vitale chooses the mixed stream of payments Option
Year
Cash Flow
Future Value Factor Formula
Future Value Factor
Future Valuie
1
$4,000
[1.04]5
1.216652902
4,866.61
2
4,000
[1.04]4
1.16985856
4,679.43
3
7,000
[1.04]3
1.124864
7,874.05
4
2,000
[1.04]2
1.0816
2,163.20
5
8,000
[1.04]1
1.04
8,320.00
Total Future Value
$ 27,903.29
Decision
Gina Vital would chooses the mixed stream of payments Option, since Gina Vital will have accumulated $ 4,214.29 more than the lump sum payment of $19,471 [ $27,903.29 – 23,689 = $4,214.29]
Year
Cash Flow
Future Value Factor Formula
Future Value Factor
Future Valuie
1
$4,000
[1.04]5
1.216652902
4,866.61
2
4,000
[1.04]4
1.16985856
4,679.43
3
7,000
[1.04]3
1.124864
7,874.05
4
2,000
[1.04]2
1.0816
2,163.20
5
8,000
[1.04]1
1.04
8,320.00
Total Future Value
$ 27,903.29
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